How does ZigBee copes up with multipath. I don't see any inherent support for channel estimation ?
In general usage Zigbee range is not very far, 10-20m, so the expected delay spreads would be less than a chip period. If the delay spread is less than a symbol (or a chip in a spread system), no equalizer is needed since the fading is flat.
For mobile use or use with longer range (e.g., higher Tx power), it is up to the implementer to determine a suitable equalization strategy. Hybrid methods using the preamble and blind equalization are possible.
I was under the impression that in DSSS systems you could choose the largest correlation peak and run with it -- at least if you've got a few distinct reflections, and not some process that's smearing the correlation peak all over.
You can do that but you'll lose performance as the SNR decreases or the multipath gets bad (e.g., more than one large peak). Usually with SS a "rake receiver" integrates multipath when it is frequency selective, but there are other methods as well.
If the fading is flat, i.e., the delay spread is shorter than a chip, you don't have to do anything.